It is expected that a pressure bump can be formed at the inner edge of a dead-zone , and where vortices can develop through the Rossby Wave Instability ( RWI ) .
It has been suggested that self-gravity can significantly affect the evolution of such vortices .
We present the results of 2D hydrodynamical simulations of the evolution of vortices forming at a pressure bump in self-gravitating discs with Toomre parameter in the range 4 - 30 .
We consider isothermal plus non-isothermal disc models that employ either the classical \beta prescription or a more realistic treatment for cooling .
The main aim is to investigate whether the condensating effect of self-gravity can stabilize vortices in sufficiently massive discs .
We confirm that in isothermal disc models with { \cal Q } \gtrsim 15 , vortex decay occurs due to the vortex self-gravitational torque .
For discs with 3 \lesssim { \cal Q } \lesssim 7 , the vortex develops gravitational instabilities within its core and undergoes gravitational collapse , whereas more massive discs give rise to the formation of global eccentric modes .
In non-isothermal discs with \beta cooling , the vortex maintains a turbulent core prior to undergoing gravitational collapse for \beta \lesssim 0.1 , whereas it decays if \beta \geq 1 .
In models that incorpore both self-gravity and a better treatment for cooling , however , a stable vortex is formed with aspect ratio \chi \sim 3 - 4 .
Our results indicate that self-gravity significantly impacts the evolution of vortices forming in protoplanetary discs , although the thermodynamical structure of the vortex is equally important for determining its long-term dynamics .